LMFDB - Embedded newform 246.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [246,2,Mod(1,246)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(246, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("246.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 246 = 2 \cdot 3 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	246.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$1.96431988972$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	246.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} +1.00000 q^{6} +2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} +1.00000 q^{6} +2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.00000 q^{10} -4.00000 q^{11} -1.00000 q^{12} -4.00000 q^{13} -2.00000 q^{14} +2.00000 q^{15} +1.00000 q^{16} -2.00000 q^{17} -1.00000 q^{18} -8.00000 q^{19} -2.00000 q^{20} -2.00000 q^{21} +4.00000 q^{22} +4.00000 q^{23} +1.00000 q^{24} -1.00000 q^{25} +4.00000 q^{26} -1.00000 q^{27} +2.00000 q^{28} -8.00000 q^{29} -2.00000 q^{30} +4.00000 q^{31} -1.00000 q^{32} +4.00000 q^{33} +2.00000 q^{34} -4.00000 q^{35} +1.00000 q^{36} +2.00000 q^{37} +8.00000 q^{38} +4.00000 q^{39} +2.00000 q^{40} -1.00000 q^{41} +2.00000 q^{42} +4.00000 q^{43} -4.00000 q^{44} -2.00000 q^{45} -4.00000 q^{46} -2.00000 q^{47} -1.00000 q^{48} -3.00000 q^{49} +1.00000 q^{50} +2.00000 q^{51} -4.00000 q^{52} +4.00000 q^{53} +1.00000 q^{54} +8.00000 q^{55} -2.00000 q^{56} +8.00000 q^{57} +8.00000 q^{58} +12.0000 q^{59} +2.00000 q^{60} -6.00000 q^{61} -4.00000 q^{62} +2.00000 q^{63} +1.00000 q^{64} +8.00000 q^{65} -4.00000 q^{66} +16.0000 q^{67} -2.00000 q^{68} -4.00000 q^{69} +4.00000 q^{70} +6.00000 q^{71} -1.00000 q^{72} -2.00000 q^{73} -2.00000 q^{74} +1.00000 q^{75} -8.00000 q^{76} -8.00000 q^{77} -4.00000 q^{78} -14.0000 q^{79} -2.00000 q^{80} +1.00000 q^{81} +1.00000 q^{82} +4.00000 q^{83} -2.00000 q^{84} +4.00000 q^{85} -4.00000 q^{86} +8.00000 q^{87} +4.00000 q^{88} -6.00000 q^{89} +2.00000 q^{90} -8.00000 q^{91} +4.00000 q^{92} -4.00000 q^{93} +2.00000 q^{94} +16.0000 q^{95} +1.00000 q^{96} -2.00000 q^{97} +3.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−2.00000	−0.894427	−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000	−0.894427	−0.447214	+	0.894427i	$0.647584\pi$
$6$	1.00000	0.408248
$7$	2.00000	0.755929	0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000	0.755929	0.377964	+	0.925820i	$0.376624\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.00000	0.632456
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	−1.00000	−0.288675
$13$	−4.00000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	−2.00000	−0.534522
$15$	2.00000	0.516398
$16$	1.00000	0.250000
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	−1.00000	−0.235702
$19$	−8.00000	−1.83533	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−8.00000	−1.83533	−0.917663	+	0.397360i	$0.869927\pi$
$20$	−2.00000	−0.447214
$21$	−2.00000	−0.436436
$22$	4.00000	0.852803
$23$	4.00000	0.834058	0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000	0.834058	0.417029	+	0.908893i	$0.363071\pi$
$24$	1.00000	0.204124
$25$	−1.00000	−0.200000
$26$	4.00000	0.784465
$27$	−1.00000	−0.192450
$28$	2.00000	0.377964
$29$	−8.00000	−1.48556	−0.742781	−	0.669534i	$-0.766494\pi$
$29$	−8.00000	−1.48556	−0.742781	+	0.669534i	$0.766494\pi$
$30$	−2.00000	−0.365148
$31$	4.00000	0.718421	0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	−1.00000	−0.176777
$33$	4.00000	0.696311
$34$	2.00000	0.342997
$35$	−4.00000	−0.676123
$36$	1.00000	0.166667
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	8.00000	1.29777
$39$	4.00000	0.640513
$40$	2.00000	0.316228
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	2.00000	0.308607
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	−4.00000	−0.603023
$45$	−2.00000	−0.298142
$46$	−4.00000	−0.589768
$47$	−2.00000	−0.291730	−0.145865	−	0.989305i	$-0.546597\pi$
$47$	−2.00000	−0.291730	−0.145865	+	0.989305i	$0.546597\pi$
$48$	−1.00000	−0.144338
$49$	−3.00000	−0.428571
$50$	1.00000	0.141421
$51$	2.00000	0.280056
$52$	−4.00000	−0.554700
$53$	4.00000	0.549442	0.274721	−	0.961524i	$-0.411414\pi$
$53$	4.00000	0.549442	0.274721	+	0.961524i	$0.411414\pi$
$54$	1.00000	0.136083
$55$	8.00000	1.07872
$56$	−2.00000	−0.267261
$57$	8.00000	1.05963
$58$	8.00000	1.05045
$59$	12.0000	1.56227	0.781133	−	0.624364i	$-0.214642\pi$
$59$	12.0000	1.56227	0.781133	+	0.624364i	$0.214642\pi$
$60$	2.00000	0.258199
$61$	−6.00000	−0.768221	−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000	−0.768221	−0.384111	+	0.923287i	$0.625492\pi$
$62$	−4.00000	−0.508001
$63$	2.00000	0.251976
$64$	1.00000	0.125000
$65$	8.00000	0.992278
$66$	−4.00000	−0.492366
$67$	16.0000	1.95471	0.977356	−	0.211604i	$-0.0678686\pi$
$67$	16.0000	1.95471	0.977356	+	0.211604i	$0.0678686\pi$
$68$	−2.00000	−0.242536
$69$	−4.00000	−0.481543
$70$	4.00000	0.478091
$71$	6.00000	0.712069	0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000	0.712069	0.356034	+	0.934473i	$0.384129\pi$
$72$	−1.00000	−0.117851
$73$	−2.00000	−0.234082	−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000	−0.234082	−0.117041	+	0.993127i	$0.537341\pi$
$74$	−2.00000	−0.232495
$75$	1.00000	0.115470
$76$	−8.00000	−0.917663
$77$	−8.00000	−0.911685
$78$	−4.00000	−0.452911
$79$	−14.0000	−1.57512	−0.787562	−	0.616236i	$-0.788657\pi$
$79$	−14.0000	−1.57512	−0.787562	+	0.616236i	$0.788657\pi$
$80$	−2.00000	−0.223607
$81$	1.00000	0.111111
$82$	1.00000	0.110432
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	−2.00000	−0.218218
$85$	4.00000	0.433861
$86$	−4.00000	−0.431331
$87$	8.00000	0.857690
$88$	4.00000	0.426401
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	2.00000	0.210819
$91$	−8.00000	−0.838628
$92$	4.00000	0.417029
$93$	−4.00000	−0.414781
$94$	2.00000	0.206284
$95$	16.0000	1.64157
$96$	1.00000	0.102062
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	3.00000	0.303046
$99$	−4.00000	−0.402015
$100$	−1.00000	−0.100000
$101$	−12.0000	−1.19404	−0.597022	−	0.802225i	$-0.703650\pi$
$101$	−12.0000	−1.19404	−0.597022	+	0.802225i	$0.703650\pi$
$102$	−2.00000	−0.198030
$103$	−20.0000	−1.97066	−0.985329	−	0.170664i	$-0.945409\pi$
$103$	−20.0000	−1.97066	−0.985329	+	0.170664i	$0.945409\pi$
$104$	4.00000	0.392232
$105$	4.00000	0.390360
$106$	−4.00000	−0.388514
$107$	4.00000	0.386695	0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000	0.386695	0.193347	+	0.981130i	$0.438066\pi$
$108$	−1.00000	−0.0962250
$109$	4.00000	0.383131	0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000	0.383131	0.191565	+	0.981480i	$0.438644\pi$
$110$	−8.00000	−0.762770
$111$	−2.00000	−0.189832
$112$	2.00000	0.188982
$113$	−18.0000	−1.69330	−0.846649	−	0.532152i	$-0.821383\pi$
$113$	−18.0000	−1.69330	−0.846649	+	0.532152i	$0.821383\pi$
$114$	−8.00000	−0.749269
$115$	−8.00000	−0.746004
$116$	−8.00000	−0.742781
$117$	−4.00000	−0.369800
$118$	−12.0000	−1.10469
$119$	−4.00000	−0.366679
$120$	−2.00000	−0.182574
$121$	5.00000	0.454545
$122$	6.00000	0.543214
$123$	1.00000	0.0901670
$124$	4.00000	0.359211
$125$	12.0000	1.07331
$126$	−2.00000	−0.178174
$127$	12.0000	1.06483	0.532414	−	0.846484i	$-0.321285\pi$
$127$	12.0000	1.06483	0.532414	+	0.846484i	$0.321285\pi$
$128$	−1.00000	−0.0883883
$129$	−4.00000	−0.352180
$130$	−8.00000	−0.701646
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	4.00000	0.348155
$133$	−16.0000	−1.38738
$134$	−16.0000	−1.38219
$135$	2.00000	0.172133
$136$	2.00000	0.171499
$137$	14.0000	1.19610	0.598050	−	0.801459i	$-0.295942\pi$
$137$	14.0000	1.19610	0.598050	+	0.801459i	$0.295942\pi$
$138$	4.00000	0.340503
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	−4.00000	−0.338062
$141$	2.00000	0.168430
$142$	−6.00000	−0.503509
$143$	16.0000	1.33799
$144$	1.00000	0.0833333
$145$	16.0000	1.32873
$146$	2.00000	0.165521
$147$	3.00000	0.247436
$148$	2.00000	0.164399
$149$	−4.00000	−0.327693	−0.163846	−	0.986486i	$-0.552390\pi$
$149$	−4.00000	−0.327693	−0.163846	+	0.986486i	$0.552390\pi$
$150$	−1.00000	−0.0816497
$151$	−18.0000	−1.46482	−0.732410	−	0.680864i	$-0.761604\pi$
$151$	−18.0000	−1.46482	−0.732410	+	0.680864i	$0.761604\pi$
$152$	8.00000	0.648886
$153$	−2.00000	−0.161690
$154$	8.00000	0.644658
$155$	−8.00000	−0.642575
$156$	4.00000	0.320256
$157$	−4.00000	−0.319235	−0.159617	−	0.987179i	$-0.551026\pi$
$157$	−4.00000	−0.319235	−0.159617	+	0.987179i	$0.551026\pi$
$158$	14.0000	1.11378
$159$	−4.00000	−0.317221
$160$	2.00000	0.158114
$161$	8.00000	0.630488
$162$	−1.00000	−0.0785674
$163$	−12.0000	−0.939913	−0.469956	−	0.882690i	$-0.655730\pi$
$163$	−12.0000	−0.939913	−0.469956	+	0.882690i	$0.655730\pi$
$164$	−1.00000	−0.0780869
$165$	−8.00000	−0.622799
$166$	−4.00000	−0.310460
$167$	6.00000	0.464294	0.232147	−	0.972681i	$-0.425425\pi$
$167$	6.00000	0.464294	0.232147	+	0.972681i	$0.425425\pi$
$168$	2.00000	0.154303
$169$	3.00000	0.230769
$170$	−4.00000	−0.306786
$171$	−8.00000	−0.611775
$172$	4.00000	0.304997
$173$	−14.0000	−1.06440	−0.532200	−	0.846619i	$-0.678635\pi$
$173$	−14.0000	−1.06440	−0.532200	+	0.846619i	$0.678635\pi$
$174$	−8.00000	−0.606478
$175$	−2.00000	−0.151186
$176$	−4.00000	−0.301511
$177$	−12.0000	−0.901975
$178$	6.00000	0.449719
$179$	20.0000	1.49487	0.747435	−	0.664335i	$-0.231285\pi$
$179$	20.0000	1.49487	0.747435	+	0.664335i	$0.231285\pi$
$180$	−2.00000	−0.149071
$181$	16.0000	1.18927	0.594635	−	0.803996i	$-0.297296\pi$
$181$	16.0000	1.18927	0.594635	+	0.803996i	$0.297296\pi$
$182$	8.00000	0.592999
$183$	6.00000	0.443533
$184$	−4.00000	−0.294884
$185$	−4.00000	−0.294086
$186$	4.00000	0.293294
$187$	8.00000	0.585018
$188$	−2.00000	−0.145865
$189$	−2.00000	−0.145479
$190$	−16.0000	−1.16076
$191$	−22.0000	−1.59186	−0.795932	−	0.605386i	$-0.793019\pi$
$191$	−22.0000	−1.59186	−0.795932	+	0.605386i	$0.793019\pi$
$192$	−1.00000	−0.0721688
$193$	22.0000	1.58359	0.791797	−	0.610784i	$-0.209146\pi$
$193$	22.0000	1.58359	0.791797	+	0.610784i	$0.209146\pi$
$194$	2.00000	0.143592
$195$	−8.00000	−0.572892
$196$	−3.00000	−0.214286
$197$	10.0000	0.712470	0.356235	−	0.934396i	$-0.384060\pi$
$197$	10.0000	0.712470	0.356235	+	0.934396i	$0.384060\pi$
$198$	4.00000	0.284268
$199$	−18.0000	−1.27599	−0.637993	−	0.770042i	$-0.720235\pi$
$199$	−18.0000	−1.27599	−0.637993	+	0.770042i	$0.720235\pi$
$200$	1.00000	0.0707107
$201$	−16.0000	−1.12855
$202$	12.0000	0.844317
$203$	−16.0000	−1.12298
$204$	2.00000	0.140028
$205$	2.00000	0.139686
$206$	20.0000	1.39347
$207$	4.00000	0.278019
$208$	−4.00000	−0.277350
$209$	32.0000	2.21349
$210$	−4.00000	−0.276026
$211$	0	0		−	1.00000i	$-0.5\pi$
$211$	0	0			1.00000i	$0.5\pi$
$212$	4.00000	0.274721
$213$	−6.00000	−0.411113
$214$	−4.00000	−0.273434
$215$	−8.00000	−0.545595
$216$	1.00000	0.0680414
$217$	8.00000	0.543075
$218$	−4.00000	−0.270914
$219$	2.00000	0.135147
$220$	8.00000	0.539360
$221$	8.00000	0.538138
$222$	2.00000	0.134231
$223$	8.00000	0.535720	0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000	0.535720	0.267860	+	0.963458i	$0.413684\pi$
$224$	−2.00000	−0.133631
$225$	−1.00000	−0.0666667
$226$	18.0000	1.19734
$227$	0	0		−	1.00000i	$-0.5\pi$
$227$	0	0			1.00000i	$0.5\pi$
$228$	8.00000	0.529813
$229$	24.0000	1.58596	0.792982	−	0.609245i	$-0.208527\pi$
$229$	24.0000	1.58596	0.792982	+	0.609245i	$0.208527\pi$
$230$	8.00000	0.527504
$231$	8.00000	0.526361
$232$	8.00000	0.525226
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	4.00000	0.261488
$235$	4.00000	0.260931
$236$	12.0000	0.781133
$237$	14.0000	0.909398
$238$	4.00000	0.259281
$239$	−10.0000	−0.646846	−0.323423	−	0.946254i	$-0.604834\pi$
$239$	−10.0000	−0.646846	−0.323423	+	0.946254i	$0.604834\pi$
$240$	2.00000	0.129099
$241$	−2.00000	−0.128831	−0.0644157	−	0.997923i	$-0.520518\pi$
$241$	−2.00000	−0.128831	−0.0644157	+	0.997923i	$0.520518\pi$
$242$	−5.00000	−0.321412
$243$	−1.00000	−0.0641500
$244$	−6.00000	−0.384111
$245$	6.00000	0.383326
$246$	−1.00000	−0.0637577
$247$	32.0000	2.03611
$248$	−4.00000	−0.254000
$249$	−4.00000	−0.253490
$250$	−12.0000	−0.758947
$251$	−20.0000	−1.26239	−0.631194	−	0.775625i	$-0.717435\pi$
$251$	−20.0000	−1.26239	−0.631194	+	0.775625i	$0.717435\pi$
$252$	2.00000	0.125988
$253$	−16.0000	−1.00591
$254$	−12.0000	−0.752947
$255$	−4.00000	−0.250490
$256$	1.00000	0.0625000
$257$	−6.00000	−0.374270	−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000	−0.374270	−0.187135	+	0.982334i	$0.559920\pi$
$258$	4.00000	0.249029
$259$	4.00000	0.248548
$260$	8.00000	0.496139
$261$	−8.00000	−0.495188
$262$	−12.0000	−0.741362
$263$	22.0000	1.35658	0.678289	−	0.734795i	$-0.262722\pi$
$263$	22.0000	1.35658	0.678289	+	0.734795i	$0.262722\pi$
$264$	−4.00000	−0.246183
$265$	−8.00000	−0.491436
$266$	16.0000	0.981023
$267$	6.00000	0.367194
$268$	16.0000	0.977356
$269$	−2.00000	−0.121942	−0.0609711	−	0.998140i	$-0.519420\pi$
$269$	−2.00000	−0.121942	−0.0609711	+	0.998140i	$0.519420\pi$
$270$	−2.00000	−0.121716
$271$	−12.0000	−0.728948	−0.364474	−	0.931214i	$-0.618751\pi$
$271$	−12.0000	−0.728948	−0.364474	+	0.931214i	$0.618751\pi$
$272$	−2.00000	−0.121268
$273$	8.00000	0.484182
$274$	−14.0000	−0.845771
$275$	4.00000	0.241209
$276$	−4.00000	−0.240772
$277$	−14.0000	−0.841178	−0.420589	−	0.907251i	$-0.638177\pi$
$277$	−14.0000	−0.841178	−0.420589	+	0.907251i	$0.638177\pi$
$278$	4.00000	0.239904
$279$	4.00000	0.239474
$280$	4.00000	0.239046
$281$	−6.00000	−0.357930	−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000	−0.357930	−0.178965	+	0.983855i	$0.557275\pi$
$282$	−2.00000	−0.119098
$283$	20.0000	1.18888	0.594438	−	0.804141i	$-0.297374\pi$
$283$	20.0000	1.18888	0.594438	+	0.804141i	$0.297374\pi$
$284$	6.00000	0.356034
$285$	−16.0000	−0.947758
$286$	−16.0000	−0.946100
$287$	−2.00000	−0.118056
$288$	−1.00000	−0.0589256
$289$	−13.0000	−0.764706
$290$	−16.0000	−0.939552
$291$	2.00000	0.117242
$292$	−2.00000	−0.117041
$293$	−32.0000	−1.86946	−0.934730	−	0.355359i	$-0.884359\pi$
$293$	−32.0000	−1.86946	−0.934730	+	0.355359i	$0.884359\pi$
$294$	−3.00000	−0.174964
$295$	−24.0000	−1.39733
$296$	−2.00000	−0.116248
$297$	4.00000	0.232104
$298$	4.00000	0.231714
$299$	−16.0000	−0.925304
$300$	1.00000	0.0577350
$301$	8.00000	0.461112
$302$	18.0000	1.03578
$303$	12.0000	0.689382
$304$	−8.00000	−0.458831
$305$	12.0000	0.687118
$306$	2.00000	0.114332
$307$	−4.00000	−0.228292	−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000	−0.228292	−0.114146	+	0.993464i	$0.536413\pi$
$308$	−8.00000	−0.455842
$309$	20.0000	1.13776
$310$	8.00000	0.454369
$311$	−14.0000	−0.793867	−0.396934	−	0.917847i	$-0.629926\pi$
$311$	−14.0000	−0.793867	−0.396934	+	0.917847i	$0.629926\pi$
$312$	−4.00000	−0.226455
$313$	−26.0000	−1.46961	−0.734803	−	0.678280i	$-0.762726\pi$
$313$	−26.0000	−1.46961	−0.734803	+	0.678280i	$0.762726\pi$
$314$	4.00000	0.225733
$315$	−4.00000	−0.225374
$316$	−14.0000	−0.787562
$317$	−12.0000	−0.673987	−0.336994	−	0.941507i	$-0.609410\pi$
$317$	−12.0000	−0.673987	−0.336994	+	0.941507i	$0.609410\pi$
$318$	4.00000	0.224309
$319$	32.0000	1.79166
$320$	−2.00000	−0.111803
$321$	−4.00000	−0.223258
$322$	−8.00000	−0.445823
$323$	16.0000	0.890264
$324$	1.00000	0.0555556
$325$	4.00000	0.221880
$326$	12.0000	0.664619
$327$	−4.00000	−0.221201
$328$	1.00000	0.0552158
$329$	−4.00000	−0.220527
$330$	8.00000	0.440386
$331$	8.00000	0.439720	0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000	0.439720	0.219860	+	0.975531i	$0.429440\pi$
$332$	4.00000	0.219529
$333$	2.00000	0.109599
$334$	−6.00000	−0.328305
$335$	−32.0000	−1.74835
$336$	−2.00000	−0.109109
$337$	18.0000	0.980522	0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000	0.980522	0.490261	+	0.871576i	$0.336901\pi$
$338$	−3.00000	−0.163178
$339$	18.0000	0.977626
$340$	4.00000	0.216930
$341$	−16.0000	−0.866449
$342$	8.00000	0.432590
$343$	−20.0000	−1.07990
$344$	−4.00000	−0.215666
$345$	8.00000	0.430706
$346$	14.0000	0.752645
$347$	−24.0000	−1.28839	−0.644194	−	0.764862i	$-0.722807\pi$
$347$	−24.0000	−1.28839	−0.644194	+	0.764862i	$0.722807\pi$
$348$	8.00000	0.428845
$349$	−26.0000	−1.39175	−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000	−1.39175	−0.695874	+	0.718164i	$0.744983\pi$
$350$	2.00000	0.106904
$351$	4.00000	0.213504
$352$	4.00000	0.213201
$353$	−30.0000	−1.59674	−0.798369	−	0.602168i	$-0.794304\pi$
$353$	−30.0000	−1.59674	−0.798369	+	0.602168i	$0.794304\pi$
$354$	12.0000	0.637793
$355$	−12.0000	−0.636894
$356$	−6.00000	−0.317999
$357$	4.00000	0.211702
$358$	−20.0000	−1.05703
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	2.00000	0.105409
$361$	45.0000	2.36842
$362$	−16.0000	−0.840941
$363$	−5.00000	−0.262432
$364$	−8.00000	−0.419314
$365$	4.00000	0.209370
$366$	−6.00000	−0.313625
$367$	8.00000	0.417597	0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000	0.417597	0.208798	+	0.977959i	$0.433045\pi$
$368$	4.00000	0.208514
$369$	−1.00000	−0.0520579
$370$	4.00000	0.207950
$371$	8.00000	0.415339
$372$	−4.00000	−0.207390
$373$	14.0000	0.724893	0.362446	−	0.932005i	$-0.381942\pi$
$373$	14.0000	0.724893	0.362446	+	0.932005i	$0.381942\pi$
$374$	−8.00000	−0.413670
$375$	−12.0000	−0.619677
$376$	2.00000	0.103142
$377$	32.0000	1.64808
$378$	2.00000	0.102869
$379$	−28.0000	−1.43826	−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000	−1.43826	−0.719132	+	0.694874i	$0.755460\pi$
$380$	16.0000	0.820783
$381$	−12.0000	−0.614779
$382$	22.0000	1.12562
$383$	−6.00000	−0.306586	−0.153293	−	0.988181i	$-0.548988\pi$
$383$	−6.00000	−0.306586	−0.153293	+	0.988181i	$0.548988\pi$
$384$	1.00000	0.0510310
$385$	16.0000	0.815436
$386$	−22.0000	−1.11977
$387$	4.00000	0.203331
$388$	−2.00000	−0.101535
$389$	−6.00000	−0.304212	−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000	−0.304212	−0.152106	+	0.988364i	$0.548606\pi$
$390$	8.00000	0.405096
$391$	−8.00000	−0.404577
$392$	3.00000	0.151523
$393$	−12.0000	−0.605320
$394$	−10.0000	−0.503793
$395$	28.0000	1.40883
$396$	−4.00000	−0.201008
$397$	−24.0000	−1.20453	−0.602263	−	0.798298i	$-0.705734\pi$
$397$	−24.0000	−1.20453	−0.602263	+	0.798298i	$0.705734\pi$
$398$	18.0000	0.902258
$399$	16.0000	0.801002
$400$	−1.00000	−0.0500000
$401$	30.0000	1.49813	0.749064	−	0.662497i	$-0.230503\pi$
$401$	30.0000	1.49813	0.749064	+	0.662497i	$0.230503\pi$
$402$	16.0000	0.798007
$403$	−16.0000	−0.797017
$404$	−12.0000	−0.597022
$405$	−2.00000	−0.0993808
$406$	16.0000	0.794067
$407$	−8.00000	−0.396545
$408$	−2.00000	−0.0990148
$409$	34.0000	1.68119	0.840596	−	0.541663i	$-0.182205\pi$
$409$	34.0000	1.68119	0.840596	+	0.541663i	$0.182205\pi$
$410$	−2.00000	−0.0987730
$411$	−14.0000	−0.690569
$412$	−20.0000	−0.985329
$413$	24.0000	1.18096
$414$	−4.00000	−0.196589
$415$	−8.00000	−0.392705
$416$	4.00000	0.196116
$417$	4.00000	0.195881
$418$	−32.0000	−1.56517
$419$	20.0000	0.977064	0.488532	−	0.872546i	$-0.337533\pi$
$419$	20.0000	0.977064	0.488532	+	0.872546i	$0.337533\pi$
$420$	4.00000	0.195180
$421$	8.00000	0.389896	0.194948	−	0.980814i	$-0.437546\pi$
$421$	8.00000	0.389896	0.194948	+	0.980814i	$0.437546\pi$
$422$	0	0
$423$	−2.00000	−0.0972433
$424$	−4.00000	−0.194257
$425$	2.00000	0.0970143
$426$	6.00000	0.290701
$427$	−12.0000	−0.580721
$428$	4.00000	0.193347
$429$	−16.0000	−0.772487
$430$	8.00000	0.385794
$431$	−8.00000	−0.385346	−0.192673	−	0.981263i	$-0.561716\pi$
$431$	−8.00000	−0.385346	−0.192673	+	0.981263i	$0.561716\pi$
$432$	−1.00000	−0.0481125
$433$	−2.00000	−0.0961139	−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000	−0.0961139	−0.0480569	+	0.998845i	$0.515303\pi$
$434$	−8.00000	−0.384012
$435$	−16.0000	−0.767141
$436$	4.00000	0.191565
$437$	−32.0000	−1.53077
$438$	−2.00000	−0.0955637
$439$	14.0000	0.668184	0.334092	−	0.942541i	$-0.391570\pi$
$439$	14.0000	0.668184	0.334092	+	0.942541i	$0.391570\pi$
$440$	−8.00000	−0.381385
$441$	−3.00000	−0.142857
$442$	−8.00000	−0.380521
$443$	−12.0000	−0.570137	−0.285069	−	0.958507i	$-0.592016\pi$
$443$	−12.0000	−0.570137	−0.285069	+	0.958507i	$0.592016\pi$
$444$	−2.00000	−0.0949158
$445$	12.0000	0.568855
$446$	−8.00000	−0.378811
$447$	4.00000	0.189194
$448$	2.00000	0.0944911
$449$	−38.0000	−1.79333	−0.896665	−	0.442709i	$-0.854018\pi$
$449$	−38.0000	−1.79333	−0.896665	+	0.442709i	$0.854018\pi$
$450$	1.00000	0.0471405
$451$	4.00000	0.188353
$452$	−18.0000	−0.846649
$453$	18.0000	0.845714
$454$	0	0
$455$	16.0000	0.750092
$456$	−8.00000	−0.374634
$457$	22.0000	1.02912	0.514558	−	0.857455i	$-0.327956\pi$
$457$	22.0000	1.02912	0.514558	+	0.857455i	$0.327956\pi$
$458$	−24.0000	−1.12145
$459$	2.00000	0.0933520
$460$	−8.00000	−0.373002
$461$	42.0000	1.95614	0.978068	−	0.208288i	$-0.0667892\pi$
$461$	42.0000	1.95614	0.978068	+	0.208288i	$0.0667892\pi$
$462$	−8.00000	−0.372194
$463$	−30.0000	−1.39422	−0.697109	−	0.716965i	$-0.745531\pi$
$463$	−30.0000	−1.39422	−0.697109	+	0.716965i	$0.745531\pi$
$464$	−8.00000	−0.371391
$465$	8.00000	0.370991
$466$	6.00000	0.277945
$467$	−12.0000	−0.555294	−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000	−0.555294	−0.277647	+	0.960683i	$0.589555\pi$
$468$	−4.00000	−0.184900
$469$	32.0000	1.47762
$470$	−4.00000	−0.184506
$471$	4.00000	0.184310
$472$	−12.0000	−0.552345
$473$	−16.0000	−0.735681
$474$	−14.0000	−0.643041
$475$	8.00000	0.367065
$476$	−4.00000	−0.183340
$477$	4.00000	0.183147
$478$	10.0000	0.457389
$479$	−14.0000	−0.639676	−0.319838	−	0.947472i	$-0.603629\pi$
$479$	−14.0000	−0.639676	−0.319838	+	0.947472i	$0.603629\pi$
$480$	−2.00000	−0.0912871
$481$	−8.00000	−0.364769
$482$	2.00000	0.0910975
$483$	−8.00000	−0.364013
$484$	5.00000	0.227273
$485$	4.00000	0.181631
$486$	1.00000	0.0453609
$487$	4.00000	0.181257	0.0906287	−	0.995885i	$-0.471112\pi$
$487$	4.00000	0.181257	0.0906287	+	0.995885i	$0.471112\pi$
$488$	6.00000	0.271607
$489$	12.0000	0.542659
$490$	−6.00000	−0.271052
$491$	−20.0000	−0.902587	−0.451294	−	0.892375i	$-0.649037\pi$
$491$	−20.0000	−0.902587	−0.451294	+	0.892375i	$0.649037\pi$
$492$	1.00000	0.0450835
$493$	16.0000	0.720604
$494$	−32.0000	−1.43975
$495$	8.00000	0.359573
$496$	4.00000	0.179605
$497$	12.0000	0.538274
$498$	4.00000	0.179244
$499$	40.0000	1.79065	0.895323	−	0.445418i	$-0.146945\pi$
$499$	40.0000	1.79065	0.895323	+	0.445418i	$0.146945\pi$
$500$	12.0000	0.536656
$501$	−6.00000	−0.268060
$502$	20.0000	0.892644
$503$	−6.00000	−0.267527	−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000	−0.267527	−0.133763	+	0.991013i	$0.542706\pi$
$504$	−2.00000	−0.0890871
$505$	24.0000	1.06799
$506$	16.0000	0.711287
$507$	−3.00000	−0.133235
$508$	12.0000	0.532414
$509$	−32.0000	−1.41838	−0.709188	−	0.705020i	$-0.750938\pi$
$509$	−32.0000	−1.41838	−0.709188	+	0.705020i	$0.750938\pi$
$510$	4.00000	0.177123
$511$	−4.00000	−0.176950
$512$	−1.00000	−0.0441942
$513$	8.00000	0.353209
$514$	6.00000	0.264649
$515$	40.0000	1.76261
$516$	−4.00000	−0.176090
$517$	8.00000	0.351840
$518$	−4.00000	−0.175750
$519$	14.0000	0.614532
$520$	−8.00000	−0.350823
$521$	30.0000	1.31432	0.657162	−	0.753749i	$-0.271757\pi$
$521$	30.0000	1.31432	0.657162	+	0.753749i	$0.271757\pi$
$522$	8.00000	0.350150
$523$	−12.0000	−0.524723	−0.262362	−	0.964970i	$-0.584501\pi$
$523$	−12.0000	−0.524723	−0.262362	+	0.964970i	$0.584501\pi$
$524$	12.0000	0.524222
$525$	2.00000	0.0872872
$526$	−22.0000	−0.959246
$527$	−8.00000	−0.348485
$528$	4.00000	0.174078
$529$	−7.00000	−0.304348
$530$	8.00000	0.347498
$531$	12.0000	0.520756
$532$	−16.0000	−0.693688
$533$	4.00000	0.173259
$534$	−6.00000	−0.259645
$535$	−8.00000	−0.345870
$536$	−16.0000	−0.691095
$537$	−20.0000	−0.863064
$538$	2.00000	0.0862261
$539$	12.0000	0.516877
$540$	2.00000	0.0860663
$541$	14.0000	0.601907	0.300954	−	0.953639i	$-0.402695\pi$
$541$	14.0000	0.601907	0.300954	+	0.953639i	$0.402695\pi$
$542$	12.0000	0.515444
$543$	−16.0000	−0.686626
$544$	2.00000	0.0857493
$545$	−8.00000	−0.342682
$546$	−8.00000	−0.342368
$547$	44.0000	1.88130	0.940652	−	0.339372i	$-0.110215\pi$
$547$	44.0000	1.88130	0.940652	+	0.339372i	$0.110215\pi$
$548$	14.0000	0.598050
$549$	−6.00000	−0.256074
$550$	−4.00000	−0.170561
$551$	64.0000	2.72649
$552$	4.00000	0.170251
$553$	−28.0000	−1.19068
$554$	14.0000	0.594803
$555$	4.00000	0.169791
$556$	−4.00000	−0.169638
$557$	−40.0000	−1.69485	−0.847427	−	0.530912i	$-0.821850\pi$
$557$	−40.0000	−1.69485	−0.847427	+	0.530912i	$0.821850\pi$
$558$	−4.00000	−0.169334
$559$	−16.0000	−0.676728
$560$	−4.00000	−0.169031
$561$	−8.00000	−0.337760
$562$	6.00000	0.253095
$563$	−24.0000	−1.01148	−0.505740	−	0.862686i	$-0.668780\pi$
$563$	−24.0000	−1.01148	−0.505740	+	0.862686i	$0.668780\pi$
$564$	2.00000	0.0842152
$565$	36.0000	1.51453
$566$	−20.0000	−0.840663
$567$	2.00000	0.0839921
$568$	−6.00000	−0.251754
$569$	6.00000	0.251533	0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000	0.251533	0.125767	+	0.992060i	$0.459861\pi$
$570$	16.0000	0.670166
$571$	−24.0000	−1.00437	−0.502184	−	0.864761i	$-0.667470\pi$
$571$	−24.0000	−1.00437	−0.502184	+	0.864761i	$0.667470\pi$
$572$	16.0000	0.668994
$573$	22.0000	0.919063
$574$	2.00000	0.0834784
$575$	−4.00000	−0.166812
$576$	1.00000	0.0416667
$577$	42.0000	1.74848	0.874241	−	0.485491i	$-0.161359\pi$
$577$	42.0000	1.74848	0.874241	+	0.485491i	$0.161359\pi$
$578$	13.0000	0.540729
$579$	−22.0000	−0.914289
$580$	16.0000	0.664364
$581$	8.00000	0.331896
$582$	−2.00000	−0.0829027
$583$	−16.0000	−0.662652
$584$	2.00000	0.0827606
$585$	8.00000	0.330759
$586$	32.0000	1.32191
$587$	12.0000	0.495293	0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000	0.495293	0.247647	+	0.968850i	$0.420343\pi$
$588$	3.00000	0.123718
$589$	−32.0000	−1.31854
$590$	24.0000	0.988064
$591$	−10.0000	−0.411345
$592$	2.00000	0.0821995
$593$	−6.00000	−0.246390	−0.123195	−	0.992382i	$-0.539314\pi$
$593$	−6.00000	−0.246390	−0.123195	+	0.992382i	$0.539314\pi$
$594$	−4.00000	−0.164122
$595$	8.00000	0.327968
$596$	−4.00000	−0.163846
$597$	18.0000	0.736691
$598$	16.0000	0.654289
$599$	20.0000	0.817178	0.408589	−	0.912719i	$-0.366021\pi$
$599$	20.0000	0.817178	0.408589	+	0.912719i	$0.366021\pi$
$600$	−1.00000	−0.0408248
$601$	−30.0000	−1.22373	−0.611863	−	0.790964i	$-0.709580\pi$
$601$	−30.0000	−1.22373	−0.611863	+	0.790964i	$0.709580\pi$
$602$	−8.00000	−0.326056
$603$	16.0000	0.651570
$604$	−18.0000	−0.732410
$605$	−10.0000	−0.406558
$606$	−12.0000	−0.487467
$607$	8.00000	0.324710	0.162355	−	0.986732i	$-0.448091\pi$
$607$	8.00000	0.324710	0.162355	+	0.986732i	$0.448091\pi$
$608$	8.00000	0.324443
$609$	16.0000	0.648353
$610$	−12.0000	−0.485866
$611$	8.00000	0.323645
$612$	−2.00000	−0.0808452
$613$	−34.0000	−1.37325	−0.686624	−	0.727013i	$-0.740908\pi$
$613$	−34.0000	−1.37325	−0.686624	+	0.727013i	$0.740908\pi$
$614$	4.00000	0.161427
$615$	−2.00000	−0.0806478
$616$	8.00000	0.322329
$617$	42.0000	1.69086	0.845428	−	0.534089i	$-0.179345\pi$
$617$	42.0000	1.69086	0.845428	+	0.534089i	$0.179345\pi$
$618$	−20.0000	−0.804518
$619$	−20.0000	−0.803868	−0.401934	−	0.915669i	$-0.631662\pi$
$619$	−20.0000	−0.803868	−0.401934	+	0.915669i	$0.631662\pi$
$620$	−8.00000	−0.321288
$621$	−4.00000	−0.160514
$622$	14.0000	0.561349
$623$	−12.0000	−0.480770
$624$	4.00000	0.160128
$625$	−19.0000	−0.760000
$626$	26.0000	1.03917
$627$	−32.0000	−1.27796
$628$	−4.00000	−0.159617
$629$	−4.00000	−0.159490
$630$	4.00000	0.159364
$631$	−8.00000	−0.318475	−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000	−0.318475	−0.159237	+	0.987240i	$0.550904\pi$
$632$	14.0000	0.556890
$633$	0	0
$634$	12.0000	0.476581
$635$	−24.0000	−0.952411
$636$	−4.00000	−0.158610
$637$	12.0000	0.475457
$638$	−32.0000	−1.26689
$639$	6.00000	0.237356
$640$	2.00000	0.0790569
$641$	30.0000	1.18493	0.592464	−	0.805597i	$-0.298155\pi$
$641$	30.0000	1.18493	0.592464	+	0.805597i	$0.298155\pi$
$642$	4.00000	0.157867
$643$	40.0000	1.57745	0.788723	−	0.614749i	$-0.210743\pi$
$643$	40.0000	1.57745	0.788723	+	0.614749i	$0.210743\pi$
$644$	8.00000	0.315244
$645$	8.00000	0.315000
$646$	−16.0000	−0.629512
$647$	12.0000	0.471769	0.235884	−	0.971781i	$-0.424201\pi$
$647$	12.0000	0.471769	0.235884	+	0.971781i	$0.424201\pi$
$648$	−1.00000	−0.0392837
$649$	−48.0000	−1.88416
$650$	−4.00000	−0.156893
$651$	−8.00000	−0.313545
$652$	−12.0000	−0.469956
$653$	48.0000	1.87839	0.939193	−	0.343391i	$-0.111576\pi$
$653$	48.0000	1.87839	0.939193	+	0.343391i	$0.111576\pi$
$654$	4.00000	0.156412
$655$	−24.0000	−0.937758
$656$	−1.00000	−0.0390434
$657$	−2.00000	−0.0780274
$658$	4.00000	0.155936
$659$	−48.0000	−1.86981	−0.934907	−	0.354892i	$-0.884518\pi$
$659$	−48.0000	−1.86981	−0.934907	+	0.354892i	$0.884518\pi$
$660$	−8.00000	−0.311400
$661$	−2.00000	−0.0777910	−0.0388955	−	0.999243i	$-0.512384\pi$
$661$	−2.00000	−0.0777910	−0.0388955	+	0.999243i	$0.512384\pi$
$662$	−8.00000	−0.310929
$663$	−8.00000	−0.310694
$664$	−4.00000	−0.155230
$665$	32.0000	1.24091
$666$	−2.00000	−0.0774984
$667$	−32.0000	−1.23904
$668$	6.00000	0.232147
$669$	−8.00000	−0.309298
$670$	32.0000	1.23627
$671$	24.0000	0.926510
$672$	2.00000	0.0771517
$673$	22.0000	0.848038	0.424019	−	0.905653i	$-0.360619\pi$
$673$	22.0000	0.848038	0.424019	+	0.905653i	$0.360619\pi$
$674$	−18.0000	−0.693334
$675$	1.00000	0.0384900
$676$	3.00000	0.115385
$677$	−2.00000	−0.0768662	−0.0384331	−	0.999261i	$-0.512237\pi$
$677$	−2.00000	−0.0768662	−0.0384331	+	0.999261i	$0.512237\pi$
$678$	−18.0000	−0.691286
$679$	−4.00000	−0.153506
$680$	−4.00000	−0.153393
$681$	0	0
$682$	16.0000	0.612672
$683$	−20.0000	−0.765279	−0.382639	−	0.923898i	$-0.624985\pi$
$683$	−20.0000	−0.765279	−0.382639	+	0.923898i	$0.624985\pi$
$684$	−8.00000	−0.305888
$685$	−28.0000	−1.06983
$686$	20.0000	0.763604
$687$	−24.0000	−0.915657
$688$	4.00000	0.152499
$689$	−16.0000	−0.609551
$690$	−8.00000	−0.304555
$691$	12.0000	0.456502	0.228251	−	0.973602i	$-0.426699\pi$
$691$	12.0000	0.456502	0.228251	+	0.973602i	$0.426699\pi$
$692$	−14.0000	−0.532200
$693$	−8.00000	−0.303895
$694$	24.0000	0.911028
$695$	8.00000	0.303457
$696$	−8.00000	−0.303239
$697$	2.00000	0.0757554
$698$	26.0000	0.984115
$699$	6.00000	0.226941
$700$	−2.00000	−0.0755929
$701$	−14.0000	−0.528773	−0.264386	−	0.964417i	$-0.585169\pi$
$701$	−14.0000	−0.528773	−0.264386	+	0.964417i	$0.585169\pi$
$702$	−4.00000	−0.150970
$703$	−16.0000	−0.603451
$704$	−4.00000	−0.150756
$705$	−4.00000	−0.150649
$706$	30.0000	1.12906
$707$	−24.0000	−0.902613
$708$	−12.0000	−0.450988
$709$	24.0000	0.901339	0.450669	−	0.892691i	$-0.351185\pi$
$709$	24.0000	0.901339	0.450669	+	0.892691i	$0.351185\pi$
$710$	12.0000	0.450352
$711$	−14.0000	−0.525041
$712$	6.00000	0.224860
$713$	16.0000	0.599205
$714$	−4.00000	−0.149696
$715$	−32.0000	−1.19673
$716$	20.0000	0.747435
$717$	10.0000	0.373457
$718$	0	0
$719$	50.0000	1.86469	0.932343	−	0.361576i	$-0.117761\pi$
$719$	50.0000	1.86469	0.932343	+	0.361576i	$0.117761\pi$
$720$	−2.00000	−0.0745356
$721$	−40.0000	−1.48968
$722$	−45.0000	−1.67473
$723$	2.00000	0.0743808
$724$	16.0000	0.594635
$725$	8.00000	0.297113
$726$	5.00000	0.185567
$727$	−42.0000	−1.55769	−0.778847	−	0.627214i	$-0.784195\pi$
$727$	−42.0000	−1.55769	−0.778847	+	0.627214i	$0.784195\pi$
$728$	8.00000	0.296500
$729$	1.00000	0.0370370
$730$	−4.00000	−0.148047
$731$	−8.00000	−0.295891
$732$	6.00000	0.221766
$733$	−46.0000	−1.69905	−0.849524	−	0.527549i	$-0.823111\pi$
$733$	−46.0000	−1.69905	−0.849524	+	0.527549i	$0.823111\pi$
$734$	−8.00000	−0.295285
$735$	−6.00000	−0.221313
$736$	−4.00000	−0.147442
$737$	−64.0000	−2.35747
$738$	1.00000	0.0368105
$739$	44.0000	1.61857	0.809283	−	0.587419i	$-0.199856\pi$
$739$	44.0000	1.61857	0.809283	+	0.587419i	$0.199856\pi$
$740$	−4.00000	−0.147043
$741$	−32.0000	−1.17555
$742$	−8.00000	−0.293689
$743$	−4.00000	−0.146746	−0.0733729	−	0.997305i	$-0.523376\pi$
$743$	−4.00000	−0.146746	−0.0733729	+	0.997305i	$0.523376\pi$
$744$	4.00000	0.146647
$745$	8.00000	0.293097
$746$	−14.0000	−0.512576
$747$	4.00000	0.146352
$748$	8.00000	0.292509
$749$	8.00000	0.292314
$750$	12.0000	0.438178
$751$	−50.0000	−1.82453	−0.912263	−	0.409605i	$-0.865667\pi$
$751$	−50.0000	−1.82453	−0.912263	+	0.409605i	$0.865667\pi$
$752$	−2.00000	−0.0729325
$753$	20.0000	0.728841
$754$	−32.0000	−1.16537
$755$	36.0000	1.31017
$756$	−2.00000	−0.0727393
$757$	−8.00000	−0.290765	−0.145382	−	0.989376i	$-0.546441\pi$
$757$	−8.00000	−0.290765	−0.145382	+	0.989376i	$0.546441\pi$
$758$	28.0000	1.01701
$759$	16.0000	0.580763
$760$	−16.0000	−0.580381
$761$	−10.0000	−0.362500	−0.181250	−	0.983437i	$-0.558014\pi$
$761$	−10.0000	−0.362500	−0.181250	+	0.983437i	$0.558014\pi$
$762$	12.0000	0.434714
$763$	8.00000	0.289619
$764$	−22.0000	−0.795932
$765$	4.00000	0.144620
$766$	6.00000	0.216789
$767$	−48.0000	−1.73318
$768$	−1.00000	−0.0360844
$769$	−30.0000	−1.08183	−0.540914	−	0.841078i	$-0.681921\pi$
$769$	−30.0000	−1.08183	−0.540914	+	0.841078i	$0.681921\pi$
$770$	−16.0000	−0.576600
$771$	6.00000	0.216085
$772$	22.0000	0.791797
$773$	−16.0000	−0.575480	−0.287740	−	0.957709i	$-0.592904\pi$
$773$	−16.0000	−0.575480	−0.287740	+	0.957709i	$0.592904\pi$
$774$	−4.00000	−0.143777
$775$	−4.00000	−0.143684
$776$	2.00000	0.0717958
$777$	−4.00000	−0.143499
$778$	6.00000	0.215110
$779$	8.00000	0.286630
$780$	−8.00000	−0.286446
$781$	−24.0000	−0.858788
$782$	8.00000	0.286079
$783$	8.00000	0.285897
$784$	−3.00000	−0.107143
$785$	8.00000	0.285532
$786$	12.0000	0.428026
$787$	4.00000	0.142585	0.0712923	−	0.997455i	$-0.477288\pi$
$787$	4.00000	0.142585	0.0712923	+	0.997455i	$0.477288\pi$
$788$	10.0000	0.356235
$789$	−22.0000	−0.783221
$790$	−28.0000	−0.996195
$791$	−36.0000	−1.28001
$792$	4.00000	0.142134
$793$	24.0000	0.852265
$794$	24.0000	0.851728
$795$	8.00000	0.283731
$796$	−18.0000	−0.637993
$797$	−42.0000	−1.48772	−0.743858	−	0.668338i	$-0.767006\pi$
$797$	−42.0000	−1.48772	−0.743858	+	0.668338i	$0.767006\pi$
$798$	−16.0000	−0.566394
$799$	4.00000	0.141510
$800$	1.00000	0.0353553
$801$	−6.00000	−0.212000
$802$	−30.0000	−1.05934
$803$	8.00000	0.282314
$804$	−16.0000	−0.564276
$805$	−16.0000	−0.563926
$806$	16.0000	0.563576
$807$	2.00000	0.0704033
$808$	12.0000	0.422159
$809$	14.0000	0.492214	0.246107	−	0.969243i	$-0.420849\pi$
$809$	14.0000	0.492214	0.246107	+	0.969243i	$0.420849\pi$
$810$	2.00000	0.0702728
$811$	28.0000	0.983213	0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000	0.983213	0.491606	+	0.870817i	$0.336410\pi$
$812$	−16.0000	−0.561490
$813$	12.0000	0.420858
$814$	8.00000	0.280400
$815$	24.0000	0.840683
$816$	2.00000	0.0700140
$817$	−32.0000	−1.11954
$818$	−34.0000	−1.18878
$819$	−8.00000	−0.279543
$820$	2.00000	0.0698430
$821$	10.0000	0.349002	0.174501	−	0.984657i	$-0.444169\pi$
$821$	10.0000	0.349002	0.174501	+	0.984657i	$0.444169\pi$
$822$	14.0000	0.488306
$823$	54.0000	1.88232	0.941161	−	0.337959i	$-0.109737\pi$
$823$	54.0000	1.88232	0.941161	+	0.337959i	$0.109737\pi$
$824$	20.0000	0.696733
$825$	−4.00000	−0.139262
$826$	−24.0000	−0.835067
$827$	−16.0000	−0.556375	−0.278187	−	0.960527i	$-0.589734\pi$
$827$	−16.0000	−0.556375	−0.278187	+	0.960527i	$0.589734\pi$
$828$	4.00000	0.139010
$829$	−26.0000	−0.903017	−0.451509	−	0.892267i	$-0.649114\pi$
$829$	−26.0000	−0.903017	−0.451509	+	0.892267i	$0.649114\pi$
$830$	8.00000	0.277684
$831$	14.0000	0.485655
$832$	−4.00000	−0.138675
$833$	6.00000	0.207888
$834$	−4.00000	−0.138509
$835$	−12.0000	−0.415277
$836$	32.0000	1.10674
$837$	−4.00000	−0.138260
$838$	−20.0000	−0.690889
$839$	30.0000	1.03572	0.517858	−	0.855467i	$-0.326730\pi$
$839$	30.0000	1.03572	0.517858	+	0.855467i	$0.326730\pi$
$840$	−4.00000	−0.138013
$841$	35.0000	1.20690
$842$	−8.00000	−0.275698
$843$	6.00000	0.206651
$844$	0	0
$845$	−6.00000	−0.206406
$846$	2.00000	0.0687614
$847$	10.0000	0.343604
$848$	4.00000	0.137361
$849$	−20.0000	−0.686398
$850$	−2.00000	−0.0685994
$851$	8.00000	0.274236
$852$	−6.00000	−0.205557
$853$	−30.0000	−1.02718	−0.513590	−	0.858036i	$-0.671685\pi$
$853$	−30.0000	−1.02718	−0.513590	+	0.858036i	$0.671685\pi$
$854$	12.0000	0.410632
$855$	16.0000	0.547188
$856$	−4.00000	−0.136717
$857$	18.0000	0.614868	0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000	0.614868	0.307434	+	0.951569i	$0.400530\pi$
$858$	16.0000	0.546231
$859$	36.0000	1.22830	0.614152	−	0.789188i	$-0.289498\pi$
$859$	36.0000	1.22830	0.614152	+	0.789188i	$0.289498\pi$
$860$	−8.00000	−0.272798
$861$	2.00000	0.0681598
$862$	8.00000	0.272481
$863$	48.0000	1.63394	0.816970	−	0.576681i	$-0.195652\pi$
$863$	48.0000	1.63394	0.816970	+	0.576681i	$0.195652\pi$
$864$	1.00000	0.0340207
$865$	28.0000	0.952029
$866$	2.00000	0.0679628
$867$	13.0000	0.441503
$868$	8.00000	0.271538
$869$	56.0000	1.89967
$870$	16.0000	0.542451
$871$	−64.0000	−2.16856
$872$	−4.00000	−0.135457
$873$	−2.00000	−0.0676897
$874$	32.0000	1.08242
$875$	24.0000	0.811348
$876$	2.00000	0.0675737
$877$	−18.0000	−0.607817	−0.303908	−	0.952701i	$-0.598292\pi$
$877$	−18.0000	−0.607817	−0.303908	+	0.952701i	$0.598292\pi$
$878$	−14.0000	−0.472477
$879$	32.0000	1.07933
$880$	8.00000	0.269680
$881$	30.0000	1.01073	0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000	1.01073	0.505363	+	0.862907i	$0.331359\pi$
$882$	3.00000	0.101015
$883$	36.0000	1.21150	0.605748	−	0.795656i	$-0.292874\pi$
$883$	36.0000	1.21150	0.605748	+	0.795656i	$0.292874\pi$
$884$	8.00000	0.269069
$885$	24.0000	0.806751
$886$	12.0000	0.403148
$887$	30.0000	1.00730	0.503651	−	0.863907i	$-0.331990\pi$
$887$	30.0000	1.00730	0.503651	+	0.863907i	$0.331990\pi$
$888$	2.00000	0.0671156
$889$	24.0000	0.804934
$890$	−12.0000	−0.402241
$891$	−4.00000	−0.134005
$892$	8.00000	0.267860
$893$	16.0000	0.535420
$894$	−4.00000	−0.133780
$895$	−40.0000	−1.33705
$896$	−2.00000	−0.0668153
$897$	16.0000	0.534224
$898$	38.0000	1.26808
$899$	−32.0000	−1.06726
$900$	−1.00000	−0.0333333
$901$	−8.00000	−0.266519
$902$	−4.00000	−0.133185
$903$	−8.00000	−0.266223
$904$	18.0000	0.598671
$905$	−32.0000	−1.06372
$906$	−18.0000	−0.598010
$907$	20.0000	0.664089	0.332045	−	0.943264i	$-0.392262\pi$
$907$	20.0000	0.664089	0.332045	+	0.943264i	$0.392262\pi$
$908$	0	0
$909$	−12.0000	−0.398015
$910$	−16.0000	−0.530395
$911$	−16.0000	−0.530104	−0.265052	−	0.964234i	$-0.585389\pi$
$911$	−16.0000	−0.530104	−0.265052	+	0.964234i	$0.585389\pi$
$912$	8.00000	0.264906
$913$	−16.0000	−0.529523
$914$	−22.0000	−0.727695
$915$	−12.0000	−0.396708
$916$	24.0000	0.792982
$917$	24.0000	0.792550
$918$	−2.00000	−0.0660098
$919$	−22.0000	−0.725713	−0.362857	−	0.931845i	$-0.618198\pi$
$919$	−22.0000	−0.725713	−0.362857	+	0.931845i	$0.618198\pi$
$920$	8.00000	0.263752
$921$	4.00000	0.131804
$922$	−42.0000	−1.38320
$923$	−24.0000	−0.789970
$924$	8.00000	0.263181
$925$	−2.00000	−0.0657596
$926$	30.0000	0.985861
$927$	−20.0000	−0.656886
$928$	8.00000	0.262613
$929$	−42.0000	−1.37798	−0.688988	−	0.724773i	$-0.741945\pi$
$929$	−42.0000	−1.37798	−0.688988	+	0.724773i	$0.741945\pi$
$930$	−8.00000	−0.262330
$931$	24.0000	0.786568
$932$	−6.00000	−0.196537
$933$	14.0000	0.458339
$934$	12.0000	0.392652
$935$	−16.0000	−0.523256
$936$	4.00000	0.130744
$937$	2.00000	0.0653372	0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000	0.0653372	0.0326686	+	0.999466i	$0.489599\pi$
$938$	−32.0000	−1.04484
$939$	26.0000	0.848478
$940$	4.00000	0.130466
$941$	10.0000	0.325991	0.162995	−	0.986627i	$-0.447884\pi$
$941$	10.0000	0.325991	0.162995	+	0.986627i	$0.447884\pi$
$942$	−4.00000	−0.130327
$943$	−4.00000	−0.130258
$944$	12.0000	0.390567
$945$	4.00000	0.130120
$946$	16.0000	0.520205
$947$	−44.0000	−1.42981	−0.714904	−	0.699223i	$-0.753530\pi$
$947$	−44.0000	−1.42981	−0.714904	+	0.699223i	$0.753530\pi$
$948$	14.0000	0.454699
$949$	8.00000	0.259691
$950$	−8.00000	−0.259554
$951$	12.0000	0.389127
$952$	4.00000	0.129641
$953$	2.00000	0.0647864	0.0323932	−	0.999475i	$-0.489687\pi$
$953$	2.00000	0.0647864	0.0323932	+	0.999475i	$0.489687\pi$
$954$	−4.00000	−0.129505
$955$	44.0000	1.42381
$956$	−10.0000	−0.323423
$957$	−32.0000	−1.03441
$958$	14.0000	0.452319
$959$	28.0000	0.904167
$960$	2.00000	0.0645497
$961$	−15.0000	−0.483871
$962$	8.00000	0.257930
$963$	4.00000	0.128898
$964$	−2.00000	−0.0644157
$965$	−44.0000	−1.41641
$966$	8.00000	0.257396
$967$	22.0000	0.707472	0.353736	−	0.935345i	$-0.384911\pi$
$967$	22.0000	0.707472	0.353736	+	0.935345i	$0.384911\pi$
$968$	−5.00000	−0.160706
$969$	−16.0000	−0.513994
$970$	−4.00000	−0.128432
$971$	44.0000	1.41203	0.706014	−	0.708198i	$-0.250492\pi$
$971$	44.0000	1.41203	0.706014	+	0.708198i	$0.250492\pi$
$972$	−1.00000	−0.0320750
$973$	−8.00000	−0.256468
$974$	−4.00000	−0.128168
$975$	−4.00000	−0.128103
$976$	−6.00000	−0.192055
$977$	−26.0000	−0.831814	−0.415907	−	0.909407i	$-0.636536\pi$
$977$	−26.0000	−0.831814	−0.415907	+	0.909407i	$0.636536\pi$
$978$	−12.0000	−0.383718
$979$	24.0000	0.767043
$980$	6.00000	0.191663
$981$	4.00000	0.127710
$982$	20.0000	0.638226
$983$	60.0000	1.91370	0.956851	−	0.290578i	$-0.0938475\pi$
$983$	60.0000	1.91370	0.956851	+	0.290578i	$0.0938475\pi$
$984$	−1.00000	−0.0318788
$985$	−20.0000	−0.637253
$986$	−16.0000	−0.509544
$987$	4.00000	0.127321
$988$	32.0000	1.01806
$989$	16.0000	0.508770
$990$	−8.00000	−0.254257
$991$	38.0000	1.20711	0.603555	−	0.797321i	$-0.293750\pi$
$991$	38.0000	1.20711	0.603555	+	0.797321i	$0.293750\pi$
$992$	−4.00000	−0.127000
$993$	−8.00000	−0.253872
$994$	−12.0000	−0.380617
$995$	36.0000	1.14128
$996$	−4.00000	−0.126745
$997$	44.0000	1.39349	0.696747	−	0.717317i	$-0.254630\pi$
$997$	44.0000	1.39349	0.696747	+	0.717317i	$0.254630\pi$
$998$	−40.0000	−1.26618
$999$	−2.00000	−0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	246.2.a.a.1.1	✓	1
3.2	odd	2		738.2.a.j.1.1		1
4.3	odd	2		1968.2.a.h.1.1		1
5.4	even	2		6150.2.a.bd.1.1		1
8.3	odd	2		7872.2.a.m.1.1		1
8.5	even	2		7872.2.a.bg.1.1		1
12.11	even	2		5904.2.a.n.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
246.2.a.a.1.1	✓	1	1.1	even	1	trivial
738.2.a.j.1.1		1	3.2	odd	2
1968.2.a.h.1.1		1	4.3	odd	2
5904.2.a.n.1.1		1	12.11	even	2
6150.2.a.bd.1.1		1	5.4	even	2
7872.2.a.m.1.1		1	8.3	odd	2
7872.2.a.bg.1.1		1	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 246 = 2 \cdot 3 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	246.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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